collated_index_mixed compute a collated index from the site indices, using a mixed model with a random site effect.

Usage

collated_index_mixed(
  data,
  s_sp,
  sindex_value = "SINDEX",
  bootID = NULL,
  boot_ind = NULL,
  glm_weights = TRUE,
  rm_zero = TRUE,
  family = c("poisson", "nbinom2"),
  habitat = NULL,
  habitat_weights = NULL,
  site_length = NULL,
  index_sites = c("all", "observed")
)

Arguments

data: data.table or data.frame Site indices per year and proportion of flight curve covered by the monitoring.
s_sp: string Species name to be found in the data.
sindex_value: string Name of the response variable, default is "SINDEX".
bootID: integer Identify the n^th bootstrap.
boot_ind: list Bootstrap samples from boot_sample.
glm_weights: logical Use the proportion of the flight curve sampled as weight, if FALSE the function uses equal weights.
rm_zero: logical Remove the sites where the species was not observed, default TRUE (they contribute 0 to the index, but are not used to estimate the distribution of the site effects).
family: character Distribution of the counts, 'poisson' (default) or 'nbinom2' (negative binomial). With 'poisson', the index matches collated_index for linked years and its level (mean count per site) is not biased by overdispersion; 'nbinom2' weights the counts differently, which can give a more precise trend but a lower level of the index.
habitat: string Name of a column of data with the habitat (or stratum) of each site, constant within site, default NULL (no habitat). The habitat is a fixed effect of the model, the site effects being the deviation of each site from the mean of its habitat (sites representative of their habitat, e.g. sampled at random within habitat strata).
habitat_weights: Weights of the habitats in the collated index: NULL (default) proportional to the number of sites of each habitat (the mean over all sites, as in collated_index), "equal" (each habitat counts equally), or a numeric vector named by habitat, e.g. the share of each habitat in the area of the region for a design stratified by habitat (normalised to sum 1).
site_length: string Name of a column of data with the length of each site (transect) in km, constant within site, default NULL. With a length, log(length) is an offset of the model and the collated index is the expected count on 1 km of transect, otherwise the expected count per site.
index_sites: character Sites the collated index is averaged over: "all" (default) all sites monitored for the species, the sites where it was never observed counting as zero, or "observed" only the sites where the species was observed at least once (habitats without such site are then left out of the index and the weights of the other habitats normalised).

Value

a list with the collated indices per year (col_index, same columns as collated_index), the site ids of the sample (site_id), the year effects (year_effect: log effect relative to the first year, LOG_EFFECT, and its standard error, SE), the model parameters (model: family, standard deviation of the site effects, size of the negative binomial, convergence) and, with habitat, the index of each habitat (habitat_index: number of sites, weight and index per habitat and year; the collated index is the weighted sum of the habitat indices).

Details

The model is the GLM of collated_index with the site effect as a random effect, round(SINDEX) ~ 0 + factor(M_YEAR) + (1 | site), weighted by the proportion of the flight curve sampled (TOTAL_NM), fitted with glmmTMB::glmmTMB() (package glmmTMB required). The collated index is defined as in collated_index, the expected index summed over the sites of the sample and divided by the number of sites of the species, exp(year effect) x sum(exp(site effects)) / number of sites, using the predicted site effects. The random site effect assumes that the sites are a sample of one population of sites. It links years that are not linked through sites with observations (column GROUP), which is valid when the sites of all groups are representative of the same population, e.g. sites assigned to years at random in a rotating panel. With linked years, the index is close to collated_index, the site effects being shrunk towards their mean. The bootstrap is used as in collated_index, with bootID and boot_ind from boot_sample. When the index is used as a density, see the section "Collated index as a density" of vignette("vignette", package = "rbms").

Author

Reto Schmucki - retoshm@ceh.ac.uk